Physics Problem Calculator

Problem

Determine the final height (H) of an object when the only force acting on it is gravity (F = mg), given its initial velocity (Vₒ), initial height (Hₒ), and final velocity (V).

Solution

We can justify the solution by considering the law of conservation of mechanical energy in the absence of friction. In this scenario, the total mechanical energy of the object remains constant, which includes both kinetic energy and potential energy.
The law of conservation of mechanical energy can be expressed as follows
E₀ = E
Where:

E₀ is the initial mechanical energy of the object, and
E is the final mechanical energy of the object.
Initial mechanical energy consists of the sum of initial kinetic energy 

K₀= ½mv₀² 

and initial potential energy 

U₀= mgh₀

The final mechanical energy consists of the sum of the final kinetic energy 

K = ½mv² 

and final potential energy 

U = mgh.

So, the law of conservation of mechanical energy can be expressed as:

½mv² + mgh = ½mv₀² + mgh₀

See the following algebraic transformation of the equation to find the expression for the unknown value: 

½mv² + mgh = ½mv₀² + mgh₀,

mv² + 2mgh = mv₀² + 2mgh₀,
v² + 2gh = v₀² + 2gh₀,
v²/(2g) + h = v₀²/(2g) + h₀,
h = v₀²/(2g) + h₀ - v²/(2g) .

Calculation

Enter the following values:

Initial Velocity Vₒ (m/s):
Initial Height Hₒ (m):
Final Velocity V (m/s):